Average Error: 62.0 → 62.0
Time: 770.0ms
Precision: 64
\[lo \lt -1.000000000000000010979063629440455417405 \cdot 10^{308} \land hi \gt 1.000000000000000010979063629440455417405 \cdot 10^{308}\]
\[\frac{x - lo}{hi - lo}\]
↓
\[\frac{x - lo}{hi - lo}\]
\frac{x - lo}{hi - lo}
↓
\frac{x - lo}{hi - lo}
double f(double lo, double hi, double x) {
        double r3810 = x;
        double r3811 = lo;
        double r3812 = r3810 - r3811;
        double r3813 = hi;
        double r3814 = r3813 - r3811;
        double r3815 = r3812 / r3814;
        return r3815;
}
↓
double f(double lo, double hi, double x) {
        double r3816 = x;
        double r3817 = lo;
        double r3818 = r3816 - r3817;
        double r3819 = hi;
        double r3820 = r3819 - r3817;
        double r3821 = r3818 / r3820;
        return r3821;
}

Error

Bits error versus lo

Bits error versus hi

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[\frac{x - lo}{hi - lo}\]

  2. Final simplification62.0

    \[\leadsto \frac{x - lo}{hi - lo}\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :precision binary64
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))